Work and Energy

Work is closely related to energy and power.

We always use the term 'Work' in our day to day life. But there is a difference in the way we use the term 'Work' in day to day life and the way we use it in the science.

In day to day life if a person solved four to five chapters of math, then it is said that he is doing hard work, but in terms of science no work is done.

Suppose a person is pushing a big rock for a long hour and that rock does not move despite all the effort. In this process he may exhausted completely. Even though on work is done on the rock, because there is no displacement of the work.

Let again assume that a person stand still for couple of hours with a heavy load on his head. He gets tired completely in this process, but still in the language of science, work done is zero.

While reading a person does only metal work and not physical. Thus, work is something different in the context of science.

On the other hand a boy is playing football for half an hour; then in the view of science work is done. But it may possible for his parent that he is not doing anything productive.

Scientific Conception of Work

Kick a football lying on a surface using your foot. The pebble moves through a distance. Here you exerted a force on the football and the football got displaced. In this situation work is done.

Take a book from the table and keep it in the book–self. Here work is done.

Thus, work to be done, there are two conditions must be needed

(a) A force should be act on an object, and

(b) The object must be displaced.

If any one of the above two conditions does not exist, work is not done. This is the way we view work in scientific way.

Definition of Work in the view of Science

Thus, work can be defined as 'When an object is displaced by exerting a force on that object, then it is said that work is done. '

Work Done By A constant Force

Let a constant force, F act on an object.

Let the object be displaced through a distance, s in the direction of the force.

Let W be the work done.

Then the product of the force and displacement is called the work.

Thus,

Work done = force × Displacement

⇒ W = F s -------- (i)

Thus, work done can be defined as, work done by a force acting on an object is equal to the magnitude of the force multiplied by the distance moved in the direction of the work.

Since, work done is the product of force applied on an object and displacement of the object. Thus, if any one of the two i.e. force or displace, be zero, then product will be zero. And work done will also become zero.

Let, force (F) = 0

And we know that, W = F × s

⇒ W = 0 × s

⇒ W = 0

Or, Let, displacement, s = 0

Then also,

W = F × 0

⇒ W = 0

Thus, in both the case, either force or displacement is zero, then work done will be zero.

Thus, both force applied on an object and displacement is equally important for work to be done.

SI Unit of Work

Similar to other quantity, work has also a unit of measurement.

We know that, SI unit of Force (F) = N (newton)

And SI unit of displacement (s) = m

And we know that,

W = F × s

Thus, by substituting the units of force (F) and displacement (s) in the formula of Work, we get

W = N m

Thus, SI unit of work is N m (Newton meter).

The unit of work N m (Newton meter) is also called Joule (J).

What is 1 J (joule) or 1 N m (newton meter) of work

If force (F) applied on the object = 1 N (newton)

And displacement (s) of the object = 1 m (meter)

Thus, Work (W) = 1 N m or J (joule)

Thus, 1 J is the amount of work done on an object when a force of 1 N displaces it by 1 m along the line of action of force.

Work is scalar or vector quantity

Work has only magnitude and no direction. Thus, work is a scalar quantity.

Example Question (1) If a force of 10 N is applied to displace an object to 5 m, then find the work done.

Solution

Here, given, Force (F) = 10 N

Displacement (s) of the object = 5 m

Then, work done (W) = ?

We know that, W = F × s or Fs

∴ W = 10 N × 5 m

⇒ W = 50 N m

Thus, work done (W) = 50 N m or 50 J Answer

Negative and Positive Work done

Work done can be either negative or positive.

Positive Work

When force is exerted in the direction of displacement of the object, the work done is positive.

Example (1)

A baby is exerted a force on a toy car in the direction of displacement.

Thus, work done (W) will be equal to the force applied (F) and displacement (s).

Or, W = F × s

Here, work done (W) is positive.

Example (2)

A foot ball is moving on the ground. A player applied a force to push the football further in the direction of movement of the football. And football again displaced to a distance.

In this case also, work done (W) = F × s

Here work done (W) is positive.

Negative Work

When the force is applied in the opposite direction of displacement, then work done is considered as negative.

Example (1)

Let a car is running with a uniform velocity in a particular direction. Driver applied a force using brakes. After a displacement car gets stop.

Here a retarding force, F is applied by driver with the help of brakes.

Here, force (F) applied is taken as negative or displacement (s) is taken as negative. And hence work done (W) is negative.

That is, W = –F × s or F × (– s)

Here, work done is negative.

Thus, when angle of direction of force and direction of displace is 180⁰, then work done will be negative.

Thus, work done is negative when the force acts opposite to the direction of displacement. And Work done is positive when the force is in the direction of displacement.

Example problem (2) If a force of 20 N is applied to an object to displace the object to 10 m. Find the work done.

Solution

Given, Force (F) = 20 N

Displacement (s) = 10 m

Thus, work done (W) = ?

We know that, W = F × s

⇒ W = 20 N × 10 m

⇒ W = 200 N m or 200 J Answer

Example Problem (3) An object is moving with a uniform velocity in east direction and a force of 15 N is applied from west direction, i.e. from opposite direction of the movement of object. Now, object stops after 5 m. Find the work done.

Given, Force (F) = – 15 N (Here since force is applied from the opposite direction, thus it is taken as negative.)

Displacement (s) = 5 m

Thus, work done (W) = ?

We know that, W = F × s

⇒ W = – 15 N × 10 m

⇒ W = – 150 N m or 7#8211; 150 J Answer

Here, work done is negative, because force is applied from the opposite direction of the displacement.

Example Problem (4) Rohit lift some books weigh 2 kg from the ground and put it on a self just above 1.5 m from the ground. Find the work done on the books.

Solution:

Given,

Mass of the books (M) = 2 kg

Displacement (s) = 1.5 m

Then Work done (W) = ?

We know that, Force (F) = mass (m) × acceleration due to gravity (g)

We know that, Acceleration due to gravity (g) = 9.8 m s^–2

Thus, Force (F) = 2 kg × 9.8 m s^–2

⇒ F = 19.6 N

Now, we know that, Work done (W) = F × s

⇒ W = 19.6 N × 1.5 m

⇒ W = 29.4 N m or 29.4 J

Thus, work done = 29.4 J Answer

Example Problem (5) A tonga is displaced upto 30 meter. If 1500 Nm work is done on tonga, then calculate the force applied by horse on tonga.

Solution

Given, Work done (W) = 1500 Nm

Displacement (s) = 30 m

Force (F) = ?

We know that, Work done (W) = Force (F) × Displacement (s)

∴ 1500 Nm = F × 30 m

⇒ F = 50 N

Thus, force (F) applied on the tonga = 50 N Answer

Example Problem (6) A 2 kg of bucket with water is drawn from a well. If the weight of water in the bucket is 8 kg and height of well is 10 meter from the water level, then find the work done on the bucket with water.

Solution

Given, mass of bucket = 2 kg

Mass of water = 8 kg

Total mass of water with bucket = 2 kg + 8 kg = 10 kg

Displacement of bucket with water, i.e. height of well from the water level (s) = 10 m

Then, work done (W) =?

We know that acceleration due to gravity (g) = 9.8 m s^–2

We know that, Weight (W) = Mass (m) × acceleration due to gravity (g)

⇒ W = 10 kg × 9.8 m s^{× 2}

⇒ W = 98 N

Or, F = 98 N [As weight is also called Force (F)]

Now, we know that, Work done (W) = Force(F) × Displacement (s)

⇒ W = 98 N × 10 m

⇒ W = 980 N m

Or, W = 980 J

Thus, work done on bucket with water = 980 J Answer